Finite Group Databasebeta

D32×D127 #30641026

order16256
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD32×D127

Splittings

FittingD32×C127 ⋊ C2
SylowC127 ⋊ C2×D32

Subgroups

subgroupG/H
centerC2D16×D127
commutator, cosocleC16×C127C23
FrattiniC16C22×D127
FittingD32×C127C2
socleC2×C127C2×D16
hypercenterD32D127
hypocenterC127C2×D32
LCSG ▷ C16×C127 ▷ C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1235 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16256, 6806);